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Mathematics > Combinatorics

Title:
Modular and p-adic cyclic codes

Abstract: This paper presents some basic theorems giving the structure of cyclic codes
of length n over the ring of integers modulo p^a and over the p-adic numbers,
where p is a prime not dividing n. An especially interesting example is the
2-adic cyclic code of length 7 with generator polynomial X^3 + lambda X^2 +
(lambda - 1) X - 1, where lambda satisfies lambda^2 - lambda + 2 =0. This is
the 2-adic generalization of both the binary Hamming code and the quaternary
octacode (the latter being equivalent to the Nordstrom-Robinson code). Other
examples include the 2-adic Golay code of length 24 and the 3-adic Golay code
of length 12.